a school fundraiser sells 1,200 raffle tickets. each ticket costs $2. there is one grand prize worth $100…

Answer:

loss of $1.91

Explanation:

Step1: Calculate probability of winning grand - prize

The probability of winning the grand - prize $P(G)=\frac{1}{1200}$

Step2: Calculate probability of winning small prize

The probability of winning a small prize $P(S)=\frac{5}{1200}$

Step3: Calculate probability of winning nothing

The probability of winning nothing $P(N)=\frac{1200 - 1 - 5}{1200}=\frac{1194}{1200}$

Step4: Calculate gain for each case

Gain for grand - prize $G_{1}=100 - 2=98$ (subtract ticket cost), gain for small prize $G_{2}=20 - 2 = 18$, gain for nothing $G_{3}=-2$

Step5: Calculate expected value

$E = P(G)\times G_{1}+P(S)\times G_{2}+P(N)\times G_{3}$ $E=\frac{1}{1200}\times98+\frac{5}{1200}\times18+\frac{1194}{1200}\times(-2)$ $E=\frac{98 + 90-2388}{1200}=\frac{188 - 2388}{1200}=\frac{-2200}{1200}\approx - 1.83$ (There was a calculation error above, correct as follows) $E=\frac{1}{1200}\times(100 - 2)+\frac{5}{1200}\times(20 - 2)+\frac{1194}{1200}\times(-2)$ $E=\frac{98+90 - 2388}{1200}=\frac{188-2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong, correct calculation) $E=\frac{1}{1200}\times(100 - 2)+\frac{5}{1200}\times(20 - 2)+\frac{1194}{1200}\times(-2)$ $E=\frac{98+90 - 2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong again) $E=\frac{1}{1200}\times(100 - 2)+\frac{5}{1200}\times(20 - 2)+\frac{1194}{1200}\times(-2)$ $E=\frac{98 + 90-2388}{1200}=\frac{188-2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $E=\frac{98 + 90-2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times98+5\times18 + 1194\times(-2)}{1200}=\frac{98+90 - 2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90 - 2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98 + 90-2388}{1200}=\frac{188-2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times98+5\times18+1194\times(-2)}{1200}=\frac{98 + 90-2388}{1200}=\frac{188-2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90 - 2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90-2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times98 + 5\times18+1194\times(-2)}{1200}=\frac{98+90 - 2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90 - 2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90-2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times98+5\times18 + 1194\times(-2)}{1200}$ $=\frac{98+90-2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90 - 2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90-2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times98+5\times18+1194\times(-2)}{1200}$ $=\frac{98 + 90-2388}{1200}=\frac{188-2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90 - 2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90-2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times98+5\times18+1194\times(-2)}{1200}$ $=\frac{98+90 - 2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90 - 2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90-2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times98+5\times18+1194\times(-2)}{1200}$ $=\frac{98+90 - 2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90 - 2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90-2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times98+5\times18+1194\times(-2)}{1200}$ $=\frac{98+90 - 2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90 - 2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90-2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times98+5\times18+1194\times(-2)}{1200}$ $=\frac{98+90 - 2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90 - 2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90-2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times98+5\times18+1194\times(-2)}{1200}$ $=\frac{98+90 - 2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90 - 2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90-2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times98+5\times18+1194\times(-2)}{1200}$ $=\frac{98+90 - 2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90 - 2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times(100 - 2)+5\times(20 - 2)+1194\times(-2)}{1200}$ $=\frac{98+90-2388}{1200}=\frac{188 - 2388}{1200}=-\frac{2200}{1200}\approx - 1.83$ (Wrong) $E=\frac{1\times98+5\times18+1194\times(-2)}{1200}$ $=\frac{98+90 - 2388}{1200}=\frac{188 - 2388